Communications in Theoretical Physics

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General Solution for Unsteady Natural Convection Flow with Heat and Mass in the Presence of Wall Slip and Ramped Wall Temperature

Saeed Ullah Jan,Sami Ul Haq,Syed Inayat Ali Shah,Ilyas Khan,Muhammad Atif Khan

Communications in Theoretical Physics, 2019, 71(6): 647-657. DOI: 10.1088/0253-6102/71/6/647

Table 1 Skin-friction for ramped temperature.

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Fig.1 Non-dimensional velocity outline along $ζ$ for various values of slip parameter $η$ corresponding to ramped temperature of plate with $τ = 0.8$ , $P r = 0.71$ , and $S c = 0.16$ .
Fig.2 Non-dimensional velocity outline for different type values of slip parameter $η$ corresponding to stepped temperature of the plate with $τ = 1.2$ , $P r = 0.71$ , and $S c = 0.16$ .
Fig.3 Non-dimensional velocity outline for different values of slip parameter $η$ corresponding to stepped and ramped temperature of the plate with $τ = 3$ , $P r = 0.71$ , and $S c = 2.01$ .
Fig.4 Non-dimensional velocity outline for various value of $N$ corresponding to ramped and stepped temperature of the plate with $τ = 3$ , $P r = 0.71$ , and $S c = 2.01$ .
Fig.5 Non-dimensional velocity outline for various value of $τ$ corresponding to ramped and stepped temperature of the plate with $η = 0.9$ , $P r = 0.71$ , and $S c = 2.01$ .
Fig.6 Non-dimensional velocity outline for various value of $S c$ corresponding to ramped and stepped temperature of the plate with $η = 0.9$ , $P r = 0.71$ , and $τ = 3$ .
Fig.7 Non-dimensional velocity outline for various value of $P r$ and $τ$ corresponding to ramped temperature of the plate with $η = 0.9$ and $N = 0.8$ .
Fig.8 Non-dimensional velocity outline for various value of $P r$ and $τ$ corresponding to stepped temperature of the plate with $η = 0.9$ and $N = 0.8$ .
Fig.9 Non-dimensional temperature outline for different values of $P r$ and $τ$ corresponding to ramped temperature of the plate.
Fig.10 Non-dimensional temperature outline for different values of $P r$ and $τ$ corresponding to stepped temperature of the plate.
Fig.11 Non-dimensional temperature outline for different values of $τ$ and $P r = 0.71$ corresponding to ramped and stepped temperature of the plate.
Fig.12 Non-dimensional concentration outline for different values of $S c$ and $τ$ corresponding to ramped temperature of the plate.
Fig.13 Modification of skin-friction $C_{f}$ for various value of slip parameter $η$ corresponding to the ramped temperature of the plate with $N = 0.8$ , $P r = 7$ , and $S c = 2.01$ .
Fig.14 Modification of skin-friction $C_{f}$ for various value of slip parameter $η$ corresponding to the stepped temperature of the plate with $N = 0.8$ , $P r = 7$ , and $S c = 2.01$ .
Fig.15 Modification of skin-friction $C_{f}$ for various value of slip parameter $η$ corresponding to the ramped and stepped temperature of the plate with $N = 0.6$ , $P r = 7$ , and $S c = 2.01$ .
Fig.16 Modification of Sherwood number $S h$ for various value of $P r$ corresponding to stepped temperature of the plate.
Fig.17 Modification of Nusselt-number $N u$ for various value of $P r$ corresponding to the ramped temperature of the plate.
Fig.18 Modification of Nusselt-number $N u$ for various value of $P r$ corresponding to the stepped temperature of the plate.
Table 2 Skin-friction for stepped temperature.
Table 3 Nusselt number for ramped temperature.
Table 4 Nusselt number for stepped temperature.
Table 5 Sherwood number.

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